Log parsing is an essential task in log analysis, and many tools have been designed to accomplish it. Existing log parsers can be categorized into statistic-based and semantic-based approaches. In comparison to semantic-based parsers, existing statistic-based parsers tend to be more efficient, require lower computational costs, and be more privacy-preserving thanks to on-premise deployment, but often fall short in their accuracy (e.g., grouping or parsing accuracy) and generalizability. Therefore, it became a common belief that statistic-based parsers cannot be as effective as semantic-based parsers since the latter could take advantage of external knowledge supported by pretrained language models. Our work, however, challenges this belief with a novel statistic-based parser, PIPLUP. PIPLUP eliminates the pre-assumption of the position of constant tokens for log grouping and relies on data-insensitive parameters to overcome the generalizability challenge, allowing "plug and play" on given log files. According to our experiments on an open-sourced large log dataset, PIPLUP shows promising accuracy and generalizability with the data-insensitive default parameter set. PIPLUP not only outperforms the state-of-the-art statistic-based log parsers, Drain and its variants, but also obtains a competitive performance compared to the best unsupervised semantic-based log parser (i.e., LUNAR). Further, PIPLUP exhibits low time consumption without GPU acceleration and external API usage; our simple, efficient, and effective approach makes it more practical in real-world adoptions, especially when costs and privacy are of major concerns.